Gilles Deleuze’s The Fold: Calculusand Curvilinear Design

Menno Hubregtse

Contents

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Deleuze’s The Fold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3The Fold and Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Greg Lynn on Folded Architecture, Blobs, and Animate Form . . . . . . . . . . . . . . . . . . . . . . . . . 6Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Abstract

This chapter addresses how Gilles Deleuze’s The Fold: Leibniz and the Baroquehas affected architectural design and theory. It summarizes key concepts inThe Fold, and it discusses how architects and architectural historians havedrawn upon this philosophical text to analyze architectural design processesand the built environment. In The Fold, Deleuze argues that Gottfried WilhelmLeibniz’s philosophy exemplifies the Baroque, the predominant style of art,architecture, and music created in Europe during the seventeenth and earlyeighteenth centuries. Leibniz’s conception of matter as forces correlates withthe curvilinearity and dynamism that characterizes this style. This overviewconcentrates on how calculus, a mathematical method that Leibniz invented in thelate seventeenth century, inspired his notions of matter, the soul, and perception.Moreover, it addresses how Deleuze interprets these concepts in The Fold, and itexplains how he uses architectural examples to clarify his arguments.

M. Hubregtse (�)Art History and Visual Studies, University of Victoria, Victoria, BC, Canadae-mail: menno@uvic.ca

© Springer Nature Switzerland AG 2020B. Sriraman (ed.), Handbook of the Mathematics of the Arts and Sciences,https://doi.org/10.1007/978-3-319-70658-0_104-1

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Shortly after The Fold was published in French in 1988, architects suchas Peter Eisenman began to create designs inspired by Leibniz’s thoughtson ontology and matter. During the 1990s, Greg Lynn employed Deleuze’sreading of Leibnizian philosophy to assess contemporary architecture and designprocesses. This chapter discusses how his publications on “folding” architecturedraw an analogy between Leibniz’s calculus-inspired notions of matter and thenew digital tools that architects were using to create and manipulate forms. Italso addresses critiques of “folding” architecture and digital design practices.

Keywords

Deleuze · Fold · Leibniz · Calculus · Architecture · Greg Lynn · CAD ·Digital design · Animate form

Introduction

Throughout history, architects have looked to philosophical texts for inspiration fortheir designs. During the 1980s, architects such as Peter Eisenman and BernardTschumi created buildings and plans based on Jacques Derrida’s writing ondeconstruction. Within a few years, Gilles Deleuze eclipsed Derrida in terms ofpopularity among architects and architectural theorists. Greg Lynn (1993a, 1996,1999), for instance, promoted Deleuze’s concepts in The Fold: Leibniz and theBaroque (1993; first published in 1988 in French as Le Pli: Leibniz et le Baroque)since they aligned with contemporary changes occurring within architectural design.During the early 1990s, architects began to use digital tools to design complexstructures, and Gottfried Wilhelm Leibniz’s notion of matter as forces is an aptmetaphor for the newfound flexibility enabled by computer software. What’s more,Leibniz’s philosophy derives from his invention of calculus, and computer-aideddesign (CAD) programs use this form of mathematics to generate and manipulateforms.

This chapter begins with an overview of the main topics in The Fold, particularlythose that pertain to calculus. Deleuze explains how Leibniz’s conception of matter,the soul, and perception relate to differential equations, and he argues that Leibniz’sphilosophy typifies the Baroque – a style that appears in the late sixteenth centuryand that characterizes European art, architecture, and music during the seventeenthand early eighteenth centuries. Deleuze refers to a range of actual and fictionalbuilding designs to illustrate Leibniz’s ideas. After a brief overview of the principalexamples of architecture and design employed in The Fold, this chapter considersother analyses of the built environment that draw upon Deleuze’s interpretation ofLeibniz’s philosophy.

The latter part of this chapter concentrates on Lynn’s publications on contempo-rary “folding” architecture which popularized ideas in The Fold among architectsand architectural theorists. It examines why Lynn draws upon Leibniz’s conceptionof matter to champion a new approach to architecture that responds to externalinfluences and that differs from Deconstructivism. Lynn also refers to Leibniz’s

Gilles Deleuze’s The Fold: Calculus and Curvilinear Design 3

philosophy and calculus in order to support his analyses of CAD design practicesand the forms they generate. This chapter concludes with an overview of the criticalassessments of Lynn’s contributions to architectural theory.

Deleuze’s The Fold

For Deleuze, Leibniz’s philosophical work, which appears in books, publishedessays, and letters, exemplifies the Baroque’s curvilinear aesthetic. Paintings,sculptures, and buildings in this style incorporate numerous dramatic curves, folds,and swirls to convey a sense of dynamism and to affect the viewers’ emotions.Deleuze, however, does not suggest that there is a causal connection betweenLeibniz’s writing and the Baroque. Rather, he demonstrates how central aspects ofLeibniz’s thoughts on matter and ontology resemble this style’s qualities. Indeed,Leibniz publishes his philosophical tracts during the late seventeenth and earlyeighteenth centuries, decades after Gian Lorenzo Bernini completed two of the mostquintessential Baroque works, the Baldacchino (1634) in St. Peter’s Basilica andthe Ecstasy of Saint Teresa (1652) in the Cornaro Chapel. Deleuze does not simplyexamine Leibniz’s philosophy with regard to Baroque cultural products. Rather, heconsiders how Leibniz’s ideas are analogous to those of modern philosophers andpoets such as Alfred Whitehead, Henri Bergson, and Stéphane Mallarmé.

Why does Deleuze equate the sculpted curves and folds of Baroque art andarchitecture with Leibniz’s philosophy? Leibniz’s ideas apropos matter, perception,and the soul mirror his mathematical conception of curvature, specifically withregard to calculus. Many of his philosophical works, such as Theodicy (1710) andMonadology (1714), were written after his discovery of calculus (he publishedhis research on differential equations in 1684). Leibniz’s notion of a tangent asan infinitesimal, a value expressed via his differential equation, resembles hisconception of matter. Deleuze notes that for Leibniz a physical entity has “coheringparts that form a fold, such that they are not separated into parts of parts but arerather divided to infinity in smaller and smaller folds that always retain a certaincohesion” (1993, 6). Moreover, a body does not consist of divisible units such asgrains of sand but resembles a piece of fabric with an infinite number of folds.What’s more, the size, shape, and motion of these folded forms of matter are definedby “the pressure of surrounding forces,” much like a tangent is defined by its curve(1993, 6).

Leibniz proposes a monist ontology that contrasts with René Descartes’s dual-istic philosophy, where the mind and body are separate entities. With regard tothe soul, Leibniz posits that it is within the body and occupies a “point of view.”Deleuze describes this point in mathematical terms: “Moving from a branching ofinflection, we distinguish a point that is no longer what runs along inflection, noris it the point of inflection itself; it is the one in which the lines perpendicular totangents meet in a state of variation. It is not exactly a point but a place, a position,a site, a ‘linear focus,’ a line emanating from lines. To the degree it representsvariation or inflection, it can be called point of view” (Deleuze 1993, 19; italics

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in original). Deleuze explains that there are an infinite number of souls, each withtheir own unique point of view. Furthermore, each point of view encompasses theentire world within it. Leibniz defines the soul as a monad, and he argues thatthe relations between monads occur according to a pre-established harmony (seeGrene and Ravetz [1962] for a mathematical interpretation of Leibniz’s proposedpre-determined system).

Each monad contains the world within itself, and this constitutes an infinitenumber of perceptions. Deleuze writes: “Since it does not exist outside of themonads that convey it, the world is included in each one in the form of perceptionsor ‘representatives,’ present and infinitely minute elements” (1993, 86; italics inoriginal). But, not all of these perceptions are consciously registered – only thosewhich are remarkable. He discusses how a differential equation allows a monad toconsciously perceive what is notable. For instance, the color green is the product of adifferential relation among blue and yellow, and Deleuze illustrates this relationshipwith the following notation: db

dy (1993, 88). Hunger becomes noticeable when it isthe product of a differential relation among parts such as “a lack of sugar, butter,etc.” (1993, 88). In short, the infinite number of minute ordinary perceptions, whichconstitute the world, are obscure and located within the perceiving monad, anddifferential relations among some of these inconspicuous elements bring forth aclear and consciously registered perception such as hunger.

The Fold and Architecture

Deleuze employs a number of architectural examples to demonstrate his theoreticalconcepts in The Fold. He refers to actual buildings as well as conceptual structuresto explain his thoughts. The most notable example is the “Baroque House (anallegory),” which appears in the first chapter (1993, 5). This architectural metaphorillustrates how the body and soul are inseparable. They occupy two floors of a housethat fold over each other. The body is located on the lower floor, and the soul ison the upper floor. The upper room has no windows, whereas the lower room hassmall openings which allow the outside world to enter as sensations. Hélène Frichot(2005) considers the Baroque House in terms of broader themes in Deleuze’s oeuvreas well as other architectural metaphors employed in his texts. Ntovros Vasileios(2009) draws upon a visual analysis of Guarino Guarini’s design for the San Lorenzoin Turin (1668–1687) to discuss the layout of Deleuze’s Baroque House and howit pertains to his arguments in The Fold. He also describes how inflection pointsand folds appear in this building’s plan and interior. When looking upward in theSan Lorenzo, Vasileios notes that the dome’s ribs lead the eye to their springingpoints, which are located above the pendentives and arches that support the dome.He posits that this space of transition between the church’s dome and lower structureis analogous to the fold that exists between the two floors in Deleuze’s BaroqueHouse.

Deleuze also draws upon contemporary design technologies to elucidate hisconcepts regarding folds, curves, and Leibniz’s calculus. He invents the word

Gilles Deleuze’s The Fold: Calculus and Curvilinear Design 5

“objectile” to refer to Bernard Cache’s investigations into industrially producedvariable non-standard forms (1993, 19; italics in original). Cache, an architect, wasworking with Patrick Beaucé and developers at Missler Software to research howdesigners could use digital tools to modulate an object’s form (Cache and Girard2013). Deleuze explains that this objectile is “manneristic, not essentializing: itbecomes an event” (1993, 19). He also refers to Cache’s insights on inflectionin Terre meuble, a manuscript that investigates furniture design with regard to“geographical” folds. It was published in English as Earth Moves (1995). Cachestudied with Deleuze at the University of Paris VIII at Vincennes-St. Denis, and henamed his architectural and digital design firm “Objectile.”

Deleuze’s The Fold has had a substantial influence on architectural design sinceits publication. Lynn (1993b, 1996, 1998, 1999) has helped circulate Deleuze’sideas on Leibniz’s philosophy among architects and architectural theorists via hisnumerous publications on folded architecture, architectural curvilinearity, blobs,and animate form. Some critics, however, have chastised the resultant foldingarchitecture as simple applications of folded forms that are not analogous withLeibniz’s philosophy or Deleuze’s ideas in The Fold (Jobst 2013; Vidler 2000).Nonetheless, Lynn’s contributions are significant in terms of this overview since heconcentrates on themes pertaining to calculus and how this mathematical methodis used in contemporary architectural design. His publications and designs arediscussed in the following section.

A number of architectural theorists and historians employ concepts in The Foldin their analyses of historic and contemporary architecture and design. Paul Harris(2005), for example, draws upon Deleuze’s notion of folds to consider SimonRodia’s Watts Towers, built in Los Angeles between 1921 and 1955. He discusseshow Rodia’s method of construction is a bottom-up process that differs from Lynn’sand Cache’s conceptions of folded architecture and design. Martin Prominski andSpyridon Koutroufinis (2009) discuss how Deleuze’s writing on the Baroque isapplicable to contemporary landscape design, and they argue that designers shouldnot simply create folded forms inspired by the French philosopher’s ideas. Theyillustrate how Carlos Ferrater and Bet Figueras’s Jardí Botànic de Barcelona,Schweingruber Zulauf’s Administration of Canton Zug, and the Versailles ÉcoleNationale Supérieure du Paysage’s plans for a flooded area in Redon recall keyconcepts in The Fold. Simon O’Sullivan (2006) relies on Deleuze’s description ofthe Baroque and his thoughts on the arts to analyze Ivan Chtcheglov’s writing onutopian cities and spaces of experimentation. Robert Porter (2009) applies ideasfrom The Fold to consider Belfast’s built environment. Don Handelman (2010)considers how Jerusalem’s security barriers, city walls, Yad Vashem museum, andSantiago Calatrava’s Chords Bridge are folded into the city’s topology and why thismatters in terms of Israeli politics and urban space. Tom Lundborg (2012) examinesthe plans for New York’s “Ground Zero” – the site of the World Trade Center towersdestroyed on September 11, 2001 – as modes of folding in response to a traumaticevent. Lundborg, however, draws upon Deleuze’s notion of folding processes basedon Michel Foucault’s philosophical tracts rather than his conception of Leibnizianfolds and calculus. Menno Hubregtse (2017) explains how Eero Saarinen’s Trans

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World Airlines Terminal at John F. Kennedy International Airport (New York, 1962)can be read in terms of Leibniz’s and Descartes’s conceptions of mathematicalcurves and matter. While the building’s curvilinear aesthetic evokes Leibniz’scalculus and a dynamic sense of matter, its non-adaptable physical structure callsto mind Descartes’s conception of geometric curves and matter as extensions inspace.

Greg Lynn on Folded Architecture, Blobs, and Animate Form

Lynn introduced Deleuze’s ideas in The Fold to a broad architectural audience inhis guest-edited March-April (1993a) issue of Architectural Design, which is titledFolding in Architecture. It includes a number of essays and short articles that exam-ine “a new pliant, flowing architecture” that started to emerge in the early 1990s(Powell 1993). Kenneth Powell’s opening essay, “Unfolding folding,” explains thatthis new “approach” departs from Postmodern and Deconstructivist architecturewhich largely focused on contradiction. Indeed, Robert Venturi’s Complexity andContradiction in Architecture (1966) prompted architects to move away fromthe Modern Movement’s functionally efficient and, typically, homogenous forms.Deconstructivist architecture, which is defined by fragmented shapes and shards,was showcased in a 1988 exhibition at the Museum of Modern Art in New York. Theshow’s curators, Philip Johnson and Mark Wigley (1988), alleged that this type ofarchitecture was subversive and shared an affinity with Russian Constructivism fromthe 1920s. What’s more, Deconstructivist architecture is also related to Derrida’sphilosophical conception of deconstruction. Two of the architects featured in theshow, Tschumi and Eisenman, collaborated with Derrida to consider how his theoryapplied to architectural design (Benjamin 1988; Derrida 1989; Eisenman 1988;Kipnis and Leeser 1997; Tschumi 1986, 1988).

The latter architect’s work appears in Lynn’s (1993a) guest-edited issue ofArchitectural Design which focuses on folding architecture. Eisenman (1991,1993a, b) describes how his design for Frankfurt’s Rebstockpark incorporates foldedforms inspired by Deleuze’s writing in The Fold (Fig. 1). He states that “the idea offolding was used on the site to initiate new social organisations of urban space and toreframe existing organisations” (1993b, 27). Powell (1993) explains that the foldingarchitecture featured in the (1993a) issue of Architectural Design was created by anumber of architects whose previous designs were Deconstructivist but who haveabandoned its confrontational approach. In Lynn’s essay for the issue, he claimsthat the “contradictory logic [of Deconstructivism] is beginning to soften in order toexploit more fully the particularities of urban and cultural contexts” (1993b, 9).

Lynn’s (1993b) article also equates Deleuze’s ideas in The Fold and René Thom’scatastrophe theory with a new type of architectural curvilinearity that respondsto external influences. He contends that the architects featured in the (1993a)issue have folded their buildings in relation to immediate political, structural,economic, and contextual concerns. Lynn suggests that this is an active processand that these folded forms are analogous to viscous fluids that morph according

Gilles Deleuze’s The Fold: Calculus and Curvilinear Design 7

Fig. 1 Eisenman Architects, Rebstockpark Masterplan, Frankfurt am Main, Germany, 1990–1992. (Image credit: Courtesy Eisenman Architects)

to their surroundings. To be sure, Lynn’s conception of architectural curvilinearityrecalls Leibniz’s conception of matter as a material defined by adjacent pressuresand forces. Lynn refers to Eisenman’s Rebstockpark to support his argument.Eisenman’s plan morphs a rectilinear building type, the siedlung housing block,in conjunction with the landscape’s contours (Fig. 1). Similarly, Frank Gehry’sGuggenheim Museum in Bilbao, Spain, employs curvilinear shapes that respond tothe city, the river, and the neighboring bridge and roadways. Lynn stresses that hisnotion of architectural curvilinearity is not merely a stylistic application of foldedforms but an approach that integrates external factors: “Rather than speak of theforms of folding autonomously, it is important to maintain a logic rather than a styleof curvilinearity. The formal affinities of these projects result from their pliancy andability to deform in response to particular contingencies” (Lynn 1993b, 14–15).

John Rajchman’s (1991) essay on the Rebstockpark competition documentsdiscusses how Eisenman’s design incorporates and exemplifies ideas in Deleuze’sLe Pli, and he notes that “electronic modeling” allows architects to create increas-ingly complex designs (62). Lynn’s (1993b) article on architectural curvilinearityexplains that architects were using computer programs to help create the formsthat evoke Deleuze’s notion of folded matter. In a retrospective essay on his(1993a) guest-edited issue of Architectural Design, Lynn (2004a) notes that hehighlighted experimental digital designs from the early 1990s which foreshadowedthe architectural forms created solely with CAD programs. Some of the architecturaldesigns featured in the (1993a) issue, however, were not formed exclusivelywith CAD technologies. Gehry, for example, drew a number of sketches for theGuggenheim Museum in Bilbao in 1991, and he used CATIA software to create adigital model and estimate construction costs (Ragheb 2001; Rappolt and Violette

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Fig. 2 Frank Gehry, Nationale-Nederlanden Building, Prague, 1992–1996. (Photo: MennoHubregtse, 2013)

2004). The Guggenheim Museum, which was completed in 1997, was the first majorcommission where Gehry employed this design process. He has used CATIA torealize the complex forms of his sketches and sculpted models for a number ofsubsequent projects. The Nationale-Nederlanden Building in Prague, which Gehrybegan to design in 1992, has a form that, like the Guggenheim Museum, respondsto its riverfront site (Figs. 2 and 3).

Lynn’s retrospective account (2004a) also explains that calculus was the primaryconcern in his analysis of architectural curvilinearity. He wrote this essay for arevised edition of Folding in Architecture (Lynn 2004b). In its preface, Helen Castle(2004) argues that digital architectural design, and its use of calculus, does notmerely indicate a technological innovation; it “represent[s] the same sort of full-scale perceptual and tectonic shift” that occurred when Filippo Brunelleschi beganto create perspectival drawings of buildings such as Florence’s Baptistery during theearly fifteenth century (7). The revised edition also contains Mario Carpo’s (2004)insights on how folding architecture had developed since the original issue waspublished in 1993. By 2004, architects were typically using CAD software to designbuildings. He explains that complex curvilinear forms are no longer prohibitivelyexpensive to build since CAD programs have reduced the cost of manufacturingnon-standard parts. Carpo alleges that the mass production of standardized buildingcomponents “began with the mechanical phase of the Industrial Revolution – and

Gilles Deleuze’s The Fold: Calculus and Curvilinear Design 9

Fig. 3 Frank Gehry,Nationale-NederlandenBuilding, Prague, 1992–1996.(Photo: Menno Hubregtse,2013)

ended with it” and that “non-standard production has opened for business and ishere to stay” (2004, 18).

Carpo also notes that the language regarding curvilinear architecture hadchanged: “Folds became blobs” (2004, 17). Here, he is referring to a new termthat Lynn began to use in 1996 to designate rounded architectural forms. In “Blobs,or why tectonics is square and topology is groovy,” Lynn (1996) considers the shapeof contemporary curved designs – such as Shoei Yoh’s roof structures – in terms ofblobs in Hollywood films as well as philosophical assessments of fluidity and form.Like his earlier essay on architectural curvilinearity (1993b), Lynn posits that blobsmeld with their environment while still retaining their own unique characteristics.He also draws an analogy between Leibniz’s monads and contemporary animationtechnologies used to model blob-like forms. In an interview with Mark Rappoltin 2003, Lynn stated that the term “blob” derived from a module in Wavefrontsoftware: “it was an acronym for Binary Large Object – spheres that could becollected to form larger composite forms” (Lynn cited in Rappolt 2003).

In Animate Form, Lynn (1999) investigates the dynamic aspect of designingarchitecture with computer visualizations and parametric modeling. He alleges thatCAD programs, which use mathematical models such as non-uniform rational basisspline (NURBS) curves, allow architects to embed virtual forces and motion withinthe constructed design: “Instead of a neutral abstract space for design, the context fordesign becomes an active abstract space that directs form within a current of forces

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that can be stored as information in the shape of the form” (1999, 11). Accordingto Lynn, CAD programs allow architects to embed temporality and flows into theirdesigns since they rely on differential equations to formulate architectural forms;buildings drawn on paper with rulers and compasses, on the other hand, simplyplot fixed coordinates in space. Lynn uses a sailboat hull as an illustrative exampleto clarify how virtual motions can be embedded into a form. The hull is modeledsuch that it planes smoothly when sailing downwind. It leans sideways and pressesagainst the water when tacking into a headwind. Even though a sailboat’s hulldoes not change as a physical object, it incorporates a number of potential motionsinto its design. Similarly, an undulating landscape contains the forces that carvedits hills and valleys, and these slopes contain virtual motions that permit objectsto roll down their surface. Like Lynn’s (1993b, 1996) analyses of architecturalcurvilinearity and blobs, he incorporates Leibniz’s ideas regarding monads, forces,and matter to support his argument: “Once design is posed within a Leibnizianmonadological space, architecture may embrace a sensibility of micro and macrocontextual specificity as a logic that can not be idealized in an abstract space offixed coordinates” (1999, 15). Lynn’s competition entry in 1994 for a gatewaythat accesses the Port Authority Bus Terminal in New York City demonstrates thisapproach (Fig. 4). Using Wavefront software, Lynn based the structure’s form onthe dynamic flows of pedestrians and vehicles (Greg Lynn Form n.d.)

Timothy Lenoir and Casey Alt (2003) consider Lynn’s early adoption of CADprograms for architectural design in terms of contemporaneous innovations inbioinformatics. They posit that his animate design process resembles “the mappingof molecular energy landscapes” as well as computer visualizations of proteinsas vectors (348). Lenoir and Alt note, however, that Lynn’s animate designshave been critiqued as a somewhat quixotic initiative since buildings are typicallystatic structures (see, for instance, Speaks 2001). No matter how many forces areaccounted for in the design process, the completed building is a fixed physicalobject. In addition, Lenoir and Alt note that some critics maintain that traditionalarchitectural design practices are as dynamic and animate as Lynn’s use of CADprograms.

Fig. 4 Greg Lynn FORM,competition entry, gatewayfor Port Authority BusTerminal, New York City,1994. (Image credit: © GregLynn FORM)

Gilles Deleuze’s The Fold: Calculus and Curvilinear Design 11

A number of architects who define their buildings as “folding architecture”claim that their designs are dynamic. In Lynn’s (1993a) guest-edited issue ofArchitectural Design, Eisenman describes the Alteka Office Building in Tokyo interms of philosophical conceptions of becoming and ontology: “The building evadesits cartesian definition: not representing an essential form, but a form ‘becoming’”(1993c, 28). Even though Eisenman’s model suggests a morphing and moving form,it does not change as a constructed physical object. Hubregtse (2017) illustrates howcomplex curvilinear designs – which connote Leibniz’s notion of matter as forces –are less dynamic than rectilinear designs when they are fabricated as built forms. Hediscusses how air terminals constructed with rectilinear modules are more adaptablethan those with complicated curved forms.

A number of overviews of CAD-designed architecture base their analyses uponLynn’s theoretical assessments of The Fold, architectural curvilinearity, blobs, andanimate form. These include investigations such as: Christian Pongratz and MariaRita Perbellini’s (2000) overview of ten architects who began practicing when CADprograms became available during the 1990s; Alicia Imperiale’s (2000) analysisof innovations in the design of architectural surfaces; Paola Gregory’s (2003)assessment of how architects are using computer visualizations to create information“scapes” for their designs; Antoine Picon’s (2010) consideration of digital designtools and their effect on the urban environment; and Carpo’s (2011) discussion ofhow architects use CAD programs and how they differ from traditional architecturaldesign practices. The tendency to associate digitally designed buildings withDeleuze’s ideas in The Fold has, in some cases, led to allegations that CAD-designedarchitecture is a new iteration of the Baroque (see, for instance, Massumi 1998).Michael Ostwald (2006) critiques this assessment, and he argues that contemporaryCAD-designed buildings share few similarities with Baroque architecture and thatthese recent examples of folding architecture are usually more characteristic ofExpressionist architecture. His analysis is based on an in-depth comparison betweenseventeenth-century Baroque buildings and contemporary structures in terms oftheir visual and material qualities as well as the social, cultural, and politicalconditions that influenced their designs. Nadir Lahiji (2016) refers to recent designssuch as Gehry’s Guggenheim Museum in Bilbao as “neobaroque,” but he arguesthat they “signify a perversion in the original philosophical idea of the Baroque”(129; italics in original).

In Ostwald’s (2006) analysis, he welcomes CAD programs for allowing archi-tects to explore and shape new forms. But, he is also apprehensive of unforeseensocial and cultural effects. Douglas Spencer (2016) argues that these new forms ofarchitecture, inspired by Deleuze’s philosophical writing, epitomize a “neoliberalideal of the post-political” (56). As noted above, Lynn draws upon The Fold to callfor an architecture that is not contradictory but folds in response to its surroundings.Spencer argues that this type of architectural approach lacks criticality and is part ofa larger trend where architectural design is merely “a service provider for the ‘real’of the market” (72). Similarly, Adrian Parr (2013) notes that Lynn and Eisenmanhave merely created new forms based on their readings of Deleuze’s philosophy;he argues that these designs do not engage with social and political issues and that

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“architects have chosen to turn a blind eye to the politics underpinning Deleuze’swork” (203). Simone Brott (1998) also alleges that Lynn’s notion of foldingarchitecture is politically ineffective, and she suggests that Derrida’s contributionsto Deconstructivism led to a more critical form architecture (see also Brott 2011).

Summary

In The Fold, Deleuze describes how calculus inspired Leibniz’s conceptions ofmatter, the soul, and perception, and he posits that Leibniz’s philosophy typifies theBaroque. The Fold has had a significant impact on architectural design and theoryas well as scholarly assessments of the built environment. Deleuze’s interpretationof Leibniz’s philosophy and calculus was published when architects were starting toexperiment with CAD software. Lynn’s publications on folding architecture theorizethe digital design process in terms of Leibniz’s calculus-inspired notions of matter,and they popularized ideas in The Fold among architects. Some critics, however,claim that folding architecture is based only a superficial application of Deleuze’sphilosophy.

Cross-References

�Baroque Architecture (Sylvie Duvernoy)� Parametric Design: Theoretical Development and Algorithmic Foundation for

Design Generation in Architecture

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